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Proofs for Andrews' Conjectures 5 and 6 on
Mohamed El Bachraoui
Folsom, Males, Rolen, and Storzer recently proved Andrews' Conjecture~4 for the coefficients of \[ v_1(q)=\sum_{n\ge 0}\frac{q^{n(n+1)/2}}{(-q^2;q^2)_n}=\sum_{n\ge 0}V_1(n)q^n. \]…
On congruence conjectures of Andrews and Bachraoui
Koustav Banerjee, Kathrin Bringmann, Mohamed El Bachraoui
Andrews and the third author recently studied congruences for certain restricted two-color partitions. They made two conjectures for Ramanujan-type congruences and a vanishing iden…
Positive Weighted Partitions Generated by Double Series
George E. Andrews, Mohamed El Bachraoui
We investigate some weighted integer partitions whose generating functions are double-series. We will establish closed formulas for these -double series and deduce that their co…
Legendre theorems for certain overpartitions and overpartition pairs
George E. Andrews, Mohamed El Bachraoui
Motivated by two Legendre-type formulas for overpartitions, we derive a variety of their companions as Legendre theorems for overpartition pairs. This leads to equalities of subcla…
Congruences for two-color partitions with odd smallest part
George E. Andrews, Mohamed El Bachraoui
For a fixed positive integer , let denote the number of two-color partitions of with odd smallest part and restrictions on even parts, and let be its gener…
Positive alternating sums of integer partitions
Mohamed El Bachraoui
We combine an extended version of Bailey's transform with an identity of Bressoud and with some identities of Berkovich and Warnaar to prove a variety of positivity results for alt…